A Statistical Model and DFT Study of the Fragmentation Mechanisms

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A Statistical Model and DFT Study of the Fragmentation Mechanisms of Metronidazole by Advanced Oxidation Processes Lejin Xu, Wuyang Li, Pierre Désesquelles, Nguyen-Thi Van-Oanh, Sébastien Thomas, and Jun Yang J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b10554 • Publication Date (Web): 10 Jan 2019 Downloaded from http://pubs.acs.org on January 11, 2019

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The Journal of Physical Chemistry

A Statistical Model and DFT Study of the Fragmentation Mechanisms of Metronidazole by Advanced Oxidation Processes

Lejin Xu1, Wuyang Li1, Pierre Désesquelles1,2,*, Nguyen-Thi Van-Oanh3, Sébastien Thomas2,3, Jun Yang1,* (L. J. Xu, W. Y. Li, P. Désesquelles, N. T. Van-Oanh, S. Thomas, J. Yang)

1

Department of Nuclear Engineering and Technology, School of Energy and

Power Engineering, Huazhong University of Science & Technology, Wuhan 430074, P. R. China 2

Centre des Sciences Nucléaires et des Sciences de la Matière (CSNSM),

Université Paris-Sud and CNRS-IN2P3, Université Paris-Saclay, bâtiment 104, 15 rue Clemenceau, F91405 Orsay Cédex, France 3

Laboratoire de Chimie Physique (LCP), CNRS UMR 8000, Université Paris-

Sud, Université Paris-Saclay, F91405 Orsay Cédex, France

* Corresponding Authors E-mail: [email protected] (P. Désesquelles) E-mail: [email protected]; [email protected] (J. Yang)

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ABSTRACT: The degradation pathway of the antibiotic metronidazole (MNZ) in waste water was investigated computationally with a physical statistical method and a quantum chemical approach. In both cases, the density functional theory (DFT) at M06-2X/6-311+G(d,p) level was used to calculate the structures and property parameters of all molecules. On the one hand, decay of the isolated MNZ molecule excited at a given excitation energy was studied using the Statistical Molecular Fragmentation (SMF) model. On the other hand, the reaction mechanisms of MNZ oxidized by hydroxyl radicals (•OH) in advanced oxidation processes (AOPs) were analyzed. Both studies show that the main reaction sites in MNZ are, by decreasing importance, –NO2, –CH2OH and – CH2CH2OH. The main degradation reactions are (i) alcohol group oxidation including the abstraction of hydrogen on C in the –CH2OH group and the oxidation of the hydroxyl group to the aldehyde and further to the carboxylic acid, and (ii) addition-elimination reactions happening on the imidazole ring which finally replace the nitro by hydroxyl radicals. The results gained are in a good agreement with the available experimental data on MNZ degradation by AOPs. The structures of intermediates, transition states and free energy surfaces are helpful in elucidating the details of the elimination mechanism, supplementing current experimental knowledge.

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INTRODUCTION Antibiotic residues have been increasingly detected in municipal wastewater, surface water, groundwater and even drinking water.1 Metronidazole (MNZ), as one of antibiotics, has been widely used for the treatment of anaerobic and protozoal infections such as trichomoniasis, amebiasis and giardiasis. It is efficient even against the most resistant of anaerobic bacteria: Bacteroides fragilis.2,

3

Due to its high solubility (7.02 g/L, in water, at 298 K), potential

mutagenicity, suspected carcinogenesis and non-biodegradability, MNZ in waste water may induce potential risk to the ecosystems and to human health,4, 5

and may favor the proliferation of antibiotic-resistant bacteria. MNZ cannot be

completely removed by sewage treatment plants (i.e., with conventional treatment methods), and thus, it is essential to design effective methods for decomposition in water. Experimental studies have already been performed to remove MNZ from aqueous solutions using adsorption/bioadsorption,6 coagulation,7 biological methods and advanced oxidation processes (AOPs) including UV, UV/H2O2, Fenton, photo-Fenton, sono-Fenton and electrochemical oxidation processes.1, 8−13

AOPs have high efficiencies and excellent performance for the removal of

antibiotics, mainly due to the production of highly oxidizing species such as hydroxyl radicals (•OH).14 With extra unpaired electrons, hydroxyl radicals are very aggressive and easy to react with a wide variety of contaminants with rate constants of the order of 106 to 109 M-1s-1.15,

16

Shemer et al.1 studied and

3



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compared the removal of MNZ via UV, UV/H2O2, H2O2/Fe2+ and UV/H2O2/Fe2+ processes. Ammar et al.12, 17 found that sono-Fenton and solar photo-Fenton processes were efficient for the mineralization of MNZ with a high degradation rate of 96%. These experimental studies mainly concentrated on the ways to accelerate and improve the degradation rate of antibiotics, by the development of novel catalysts, the optimization of reaction conditions and the analysis of reaction kinetics. However, the detailed degradation mechanisms have not been exhaustively explored and couldn’t reach a consensus. The fragmentation mechanisms and degradation pathways of antibiotics are currently assessed using various instrumental analyses, such as highperformance liquid chromatography with mass spectrometry (HPLC/MS), gas chromatography/mass spectrometry (GC/MS), and GC/MS/MS.18−20 Under various experimental operations, there is some controversy over the degradation pathways of antibiotics by AOPs which are deduced according to the different intermediates with steady state detected. Pérez et al.18 proposed a reaction pathway for MNZ mineralization based on heterocyclic intermediates and

hydroxylated

derivatives

photoelectron-Fenton

process.

identified

by

LC/MS

during

was

destroyed

Metronidazole

the

solar

through

hydroxylation with denitration and oxidation of the lateral N-ethanol to N-acetic acid group, forming 3-(2-hydroxy-ethyl)-2-methyl-3H-imidazol-4-ol and (2methyl-5-nitro-imidazol-1-yl) acetic acid (Table 1), respectively, which were further oxidized to (5-hydroxy-2-methyl-imidazol-1-yl) acetic acid by the action 4


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of •OH. However, based on the macromolecular intermediate products of MNZ detected by GC/MS during the electrochemical oxidation, Dai et al.19 speculated that part of the MNZ decomposed to 1H-imidazole (Table 1) via hydroxyethyl cleavage and N-denitration, and the others were oxidized to (5-hydroxy-1Himidazol-1-yl) acetic acid (Table 1) through hydroxyl substitution by the attack of •OH. Thus, the diversity of the candidate mechanisms proposed by these authors shows that it is far from enough to study the mechanisms and degradation pathways of antibiotics by AOPs only through experiments. Table 1 The degradation pathways have also been studied using theoretical models. Density functional theory (DFT) is often used to calculate the structural formula and energy barriers during the degradation process of organics as it is an effective approach to study the electronic properties and the reaction mechanisms. By means of DFT calculations, He’s group21−23 investigated the reaction mechanisms of 2,4,6-trinitrotoluene (TNT), 2,4-dinitrotoluene (DNT) and 2,4-dinitroanisole with hydroxyl radicals for advanced oxidation processes. Hydroxide degradation pathways for imidazolium cations were studied computationally, and the associated energy barriers were calculated by DFT.24, 25

In this paper, we used a physical statistical model combined with a DFT study to explore the early stage fragmentation mechanisms of MNZ. The primary cleavage products of MNZ were calculated using the Statistical Molecular 5



Fragmentation (SMF) model. Moreover, the reaction mechanisms of MNZ with •OH for AOPs were simulated using DFT based on the references given by experiments. The information gained by these simulations is helpful in elucidating the detailed fragmentation mechanisms and supplementing current experimental knowledge.

THEORETICAL METHODS The SMF model. Up to now, there were neither fragmentation models nor chemical kinetic models capable of investigating the molecular fragmentation mechanisms to provide sufficiently generic and reliable predictions for experimental results. Since the beginning of physical chemistry, statistical physics schemes have been used to describe molecular fragmentation processes.26−28 Désesquelles and coworkers have developed the SMF model, which was adapted from schemes of the Microcanonical Metropolis Monte Carlo (MMMC) model29 developed by Gross30 to simulate atomic nuclei multifragmentation, and latter adapted to the fragmentation of atomic clusters31−34. This unimolecular fragmentation model calculates, as a function of the excitation energy deposit in the parent molecule, the probabilities of all possible fragmentation channels, together with the average kinetic energies and excitation energy of the daughter molecules. The model follows a microcanonical microscopic statistical approach. The system is treated in the microcanonical ensemble at thermodynamic equilibrium and subjected to a 6


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given initial excitation energy. This statistical approach is numerically implemented in consideration of all possible configurations of isomers, geometries and electronic ground and lowlying excited states of the fragments. The probabilities of the fragmentation channels depend on the corresponding phase space volumes constrained by the conservation laws of elements, total energy and linear and angular momentum. The branching ratios of the fragmentation channels are in proportion to the products of the statistical weights that correspond to the different degrees of freedom of the system. The structural properties of the parent and daughter molecules are obtained from quantum ab initio electronic structure calculations, which are essential in the SMF model. The SMF model takes into account all possible fragmentation channels35 which are generated by scanning recursively all combinations of broken and un-broken bonds in the parent molecule (i.e., MNZ). For an n bond molecule, this corresponds to 2n primary combinations; that means more than 2 million for MNZ. However, due to the molecular symmetry, many of them are equivalent. After all possible fragmentation channels of the parent molecule have been listed, the next step involves scanning all possible combinations of shape conformations and electronic ground and low-lying excited states of daughter fragments. To calculate the fragmentation channel probability, the combinatorial weight must first be multiplied by the product of electronic spin multiplicity and angular 7



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momentum multiplicity. For each fragment, the phase space also includes 3 dimensions for linear momentum and fr (number of rotational degrees of freedom) dimensions for angular momentum. Finally, the available energy is defined as the initial excitation energy minus the binding energy of the fragmentation channel. The energy weight of a fragmentation channel is the convolution of the available energy between the dynamic degrees of freedom: the translational and rotational dynamic energies and the vibrational energies of the fragments. The vibrational level density is assumed to be that of the separable harmonic oscillators. The calculation of the series of fragmentation channel

weights

requires

the

knowledge

of

the

following

physical

characteristics of the parent molecule and its fragments: mechanic features (including mass and principal inertia momenta), quantum numbers (including spin and angular momentum multiplicities), molecular graph (including chemical composition, symmetry group, number of vibrational and rotational degrees of freedom) and energetic features (including electronic and vibrational energies for the ground and low-lying excited states and minimum bond dissociation energy: BDE). In this study, the values of these physical characteristics of MNZ and its fragments are obtained, using quantum chemical calculations based on density functional theory, with the Gaussian 16 software package.36 The structures were optimized at the M06-2X/6-311+G(d,p) level.37 The M06-2X functional was chosen for its widely recognized high quality about main group elements especially for their chemical thermodynamics.37 As input 8


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information, the SMF model also requires a distribution of excitation energy deposited in the MNZ. Alternatively, the energy distribution could be deduced from the experimental observables by solving the inverse problem.38−40 In this work, all possible values of the excitation energy were considered in the energy low range. In the following, we focus on the low energy domain, bounded by the three-fragment threshold (given by SMF as equal to 115 kcal/mol) since our goal is to study the fragmentation of MNZ, and to analyze its efficient reduction, which means that only non-toxic daughter molecules are produced using a minimum amount of energy.

Transition state calculations. The SMF model considers isolated molecules. In this part of our work, we consider the effects of the water medium on the transition paths. The dynamics of the degradation of metronidazole were studied using the same basis at M06-2X/6-311+G(d,p). Because the function M06-2X has been successfully used to study the alkaline hydrolysis of trinitrotoluene and other similar organics,41−43 it is also used in this study considering that MNZ has the same functional groups (-NO2, -OH, -CH3), similar molecular weight (almost 200) and analogous reactions with hydroxyls. All stationary points were further identified by frequency analysis as local minima (intermediates, no imaginary frequencies) or transition states (TS: saddle points, with only one virtual frequency). The Mulliken charge distribution was gathered at the same theory level as geometry optimization. Zero-point vibrational 9



energies, corrections to entropy, enthalpy, and Gibbs free energy were also ascertained. The BDE was calculated by the equation: ∆H(A-B) = H(A)+H(B)-H(AB), where H is the sum of electronic and thermal enthalpies. The intrinsic reaction coordinate (IRC) path was tracked to ensure that each TS was connected to the energy profiles of the two related minima of the proposed mechanism.44 Meanwhile, a self-consistent reaction field (SCRF) calculation using the solvation model based on density (SMD)45 was chosen to simulate the effect of water. The activation Gibbs free energies (∆G) of all considered species were computed by the standard expression of ∆G = ∆H-T∆S at T = 298.15 K, where ∆H and ∆S are the activation enthalpy and entropy, respectively. These activation ∆G energies contain free energy corrections due to the SMD solvation model. All structures were visualized using the GaussView 6.0 software.46

RESULTS AND DISCUSSION Fragmentation of MNZ. The geometric structure, atom labels, bond lengths and bond energies of MNZ are shown in Fig. 1. The lengths of C1-N3, N2-C14, C9-C10, C14-C17 and C17−O20 bonds are 1.42, 1.46, 1.49, 1.52 and 1.42 Å, respectively. Covalent bonds, usually less stable or weaker when the bond length is longer,47 which can be broken more easily by external stimuli.48 Based on the BDE data, one expects the most important fragmentation channels to be the breakage of the C1-N3, C14-C17, and N2-C14 bonds. Furthermore, abstraction 10


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of hydrogen from C17 should be favored over that of O20. All possible fragmentation channels of MNZ and its fragments as well as all possible combinations of shape conformations and spin multiplicities have been considered by the SMF model. The data used in the SMF calculations are summarized in Table 2. Fig. 1 Table 2 The evolution, at low MNZ excitation energy, of the fragmentation channel statistical weights, is presented in Fig. 2. It can be noticed that the model evaluates MNZ fragmentation weights over more than two hundred orders of magnitude, which is necessary for the calculation of the probabilities close to the two-fragment channel thresholds. Each weight function is characterized by an initial rapid increase due to the opening of the phase space dimensions corresponding both to the excitation energies of the fragments and to the kinetic degrees of freedom. The curve flattens when the available excitation energy becomes larger than the sum of the binding energies of the fragments. The fragmentation channel on the left hand side of the figure, that is the un-broken MNZ, shows only the first behavior as it cannot transfer initial excitation into kinetic energy. Fig. 2 The normalization, energy-wise, of each weight by the sum of all the weights, gives the probabilities of the fragmentation channels as shown in Fig. 3. As can 11



be seen, most of the channels have very small probabilities; at low excitation energy, only 4 fragmentation channels out of 12 have sizable probabilities. Fig. 3 The minimum dissociation energy of MNZ is 82.7 kcal/mol. As the isolated molecule has no translation or rotation degrees of freedom, the first fragmentation yield, d4,5+O, probability is instantly equal to 1 as it is the only possible fragmentation channel, whereas its statistical weight is extremely low. This fragmentation channel corresponds to the loss of an oxygen atom (number 4 or 5 in Fig. 1) from the nitro group. Its excitation energy range is very narrow (less than 1 kcal/mol), because O has neither internal nor rotational degrees of freedom. Therefore, in practice, this fragmentation channel should play little role except if the MNZ is excited in this specific range by a mono energetic photon beam or by radiative reactions such as quenching.49 The main fragmentation channel at low energy appears to be nitrogen dioxide emission, d3+NO2, as noted before, due to a low threshold energy (d3 has the highest specific enthalpy, ∆h = 62.3 kJ/kg, among the di molecules, here ∆h is used as a measure of the atomization energy of the molecule normalized by its molecular mass) and relatively high binding energies. The threshold for d17+CH2OH is very close to the previous fragmentation channel. Initially, both yields are parallel until the latter catches up with the former due mostly to the higher value of the product of its fragment state densities. Therefore, the small difference in dissociation energy, about 1.7 kcal/mol (Fig. 2), results into a 17 kcal/mol shift 12


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(Fig. 3) of the observable probability thresholds. The dissociation energy for the third fragmentation channel, d14+CH2CH2OH, is also close to the first two ones (5 kcal/mol difference, Fig. 2). It overcomes the nitrogen dioxide emission only over 160 kcal/mol mostly due to the much higher number of vibrational degrees of freedom of CH2CH2OH (18) with respect to NO2. Due to the stability of CH3 in vacuum and to the relatively long length of the C9-C10 bond, fragmentation channel d10+CH3 would be expected to have high probability. The model shows the opposite (Fig. 2). This is mainly a consequence of the low specific enthalpy of d10 (∆h = 48.8 kJ/kg, the lowest among the di molecules) which entails a high threshold energy for this channel. An important result is that the SMF model implies that first three bonds to cleave on MNZ are the C1-N3, N2-C14 and C14C17 bonds, which are also the most probable locations for chemical reactions, following the experimental observations.12, 17, 19 The other fragmentation yields, i.e. d11 + H, d20 + HO, d18 + H, d15 +H, d21 + H, d10 + CH3 and d7 + H, while energetically possible, are extremely unlikely. Consequently, the model predicts that, below 115 kcal/mol (i.e. the threshold for three-fragment fragmentation channels), neither hydrogen atoms nor CH3 molecules are produced in the fragmentation of isolated metronidazole. Thus, fragmentation will not induce the production of H2 nor CH4 molecules in the aqueous phase.

Initial steps in the reactions of MNZ with •OH. Considering that 13



AOPs are efficient for the degradation of MNZ, and that AOPs can mostly be attributed to the attack of •OH, the following work mainly focuses on the reaction mechanisms of MNZ with •OH. Hydroxyl radicals attack organic molecules by either hydrogen-abstraction on saturated organic compounds, addition to double bonds with unsaturated organic compounds or one-electron oxidation.50−52 Considering the complementarity and similarity between the fragmentation process and chemical reactions, that is, both processes have a bond breaking process, a static and a dynamic description, i.e., the SMF model and DFT calculations, are combined to explore the degradation pathways of MNZ. Following the results calculated by the SMF model, the breaking of C14−C17, C1−N3 and N2−C14 bonds are the most probable processes at low excitation energy. Combined with the intermediate molecules identified using LC/MS in experiments, 3-(2-hydroxy-ethyl)-2-methyl-3H-imidazol-4-ol, (2methyl-5-nitroimidazol-1-yl) acetic acid, (5-hydroxyl-2-methyl-imidazol-1-yl) acetic acid, 2-methyl-5-nitro-1H-imidazole, 2-methyl-3H-imidazol-4-ol, 1-(2hydroxyethyl)-2-methyl-5-aminoimidazole and 1-(2-hydroxyethyl)-2-methyl-5imidazole were detected, and 1H-imidazol-5-ol was deduced as listed in Table 1.10, 12, 18, 53, 54 Therefore, we propose the rough primary reaction pathways of MNZ with •OH, as shown in Fig. 4. The two main pathways for the initial steps of MNZ reacting with •OH are hydrogen-abstraction from the alcohol group −CH2OH (pathway i) and •OH addition to the unsaturated ring (pathway ii). The difference is that •OH attacks the C atom or O atom on the side chain for the 14


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alcohol group oxidation while •OH attacks the C atoms or N atoms on the ring chain for the addition reaction. Then, we will study how MNZ is decomposed by •OH to (2-methyl-5-nitroimidazol-1-yl) acetic acid, (5-hydroxy-2-methylimidazol-1-yl) acetic acid and 1-(2-hydroxyethyl)-5-nitro-1H-imidazol-2-ol, which are the degradation products at the early stage of reactions. The calculation about the replacement of –CH3 by •OH was conducted to check whether it is easier for •OH to react with –NO2 than with –CH3, and to see if the presence of water changes the mechanism calculated from statistical physics in vacuum by SMF. In addition, the removal process of –CH2CH2OH was also considered. Fig. 4

Alcohol group oxidation. The detailed reaction mechanisms for the oxidation of the alcohol group by •OH (pathway i in Fig. 4) are calculated and shown in Fig. 5. The first step, from species 0 to 2, can be divided into two pathways, that is, abstracting the hydrogen atom of the hydroxyl group (IN1) and abstracting the hydrogen atom of the primary methylene attached to the hydroxyl group (IN1’), respectively. The whole path from 0 (MNZ) to 3 is composed of two hydrogen-abstraction reactions and three dehydration reactions. The geometries of TS and the profiles of ΔG for the whole pathways are drawn in Fig. 6 and Fig. 7, respectively. As shown in Fig. 6, the lengths of the O-H or C-H breaking bonds and H-O forming bonds are 1.08 Å and 1.27 Å 15



at TS0, 1.15 Å and 1.51 Å at TS0’, and 1.15 Å and 1.55 Å at TS2, respectively, indicating that the hydrogen-abstraction reaction by •OH is a simple asynchronous atom-transfer reaction in which the new O-H bond substitutes for the old O-H or C-H bond. For the dehydration reactions, the lengths of the two H-C(l1) and O-O(l3) breaking bonds at TS1 are 1.26 Å and 1.87 Å, and those of the C-O(l1) and O-H(l3) breaking bonds at TS1’ are 1.52 Å and 1.37 Å, respectively. It indicates that the dehydration reaction, as an asynchronous process, first breaks two bonds and later forms one bonds. Fig. 5 Fig. 6 Fig. 7 In detail, the two pathways for the first hydrogen-abstraction of MNZ have evident differences: the top one in Fig. 7 needs to overcome a barrier of 59.6 kcal/mol to form the radical of IN1, while the bottom one only needs 5.3 kcal/mol to form IN1’ (Table 3). The difference (∆G0-IN1 is more than 10 times ∆G0-IN1’) may result in very different reaction rates. This is consistent with the observation that, for most aliphatic compounds, the reaction of •OH with H atom combined with oxygen (H21 in Fig. 1) is less probable than that combined with carbon (H18 or H19 in Fig. 1).16 The next two combinations of two radicals (IN1 or IN1’ and •OH) are diffusion-controlled processes without energy barrier. However, the reaction energy gap between these two steps is substantial: -26.7 kcal/mol for ∆GR1 and -85.3 kcal/mol for ∆GR1’. This may result from the bond 16


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energy difference between O-O and C-O. The subsequent dehydration reactions also show an obvious difference in energy barriers that are 57.2 kcal/mol for path 1→2 and 39.1 kcal/mol for path 1’→2, respectively. However, the reaction energy gaps have opposite results, which are -67.2 kcal/mol for path 1→2 and 2.1 kcal/mol for path 1’→2, respectively. Compared to the large energy gaps of the previous addition reactions, this obstacle is easily overcome. For these reasons, the path 0→IN1’→1’→2 will be energetically more favorable. This is consistent with the prediction from the SMF model. The next Habstraction from the -CHO group only needs to overcome a 3.2 kcal/mol barrier and then form the -CO radical, which will combine with a hydroxyl radical and release a 94.4 kcal/mol energy similar to IN1’→1’ (85.3 kcal/mol) because both of them form the same bond (C-O). In a word, the oxidation of the alcohol group on MNZ by •OH is a spontaneous exothermic reaction. Table 3

Addition-elimination

reactions.

The

MNZ

molecule

includes

two

unsaturated bonds, namely C1=C6 and C9=N8 on the imidazole ring. Hydroxyl radical, as a strong oxidizing agent (E0=2.8 V/SHE at pH=0), can easily be added to the unsaturated bonds due to the unpaired electrons of the oxygen atoms. In subsequent investigations, the addition of hydroxyl radicals at different positions on the imidazole ring was calculated (pathway ii in Fig. 4), and we focused mainly on the total molecular energy. The free energies and 17



geometries of four isomeric intermediates corresponding to the addition of a single •OH radical, are given in Fig. 8. When a hydroxyl radical is added to the C atoms, the generated energy of the radical adduct is negative, indicating that it forms a more stable product. The Mulliken charges shown in Fig. 1 indicates that C1, C6 and C9 atoms have positive charges while the N8 atom has a negative charge (-0.085). The difference between C atoms and the N atom is that all three C atoms have a substituent (nitro, methyl and hydrogen), which is the main reason why hydroxyl radicals are more likely to be added to C atoms. In the following, the primary methyl and nitro elimination reactions will be studied in detail. Fig. 8

Methyl elimination reaction. As shown in Fig. 9, we designed four routes (Paths I, II, III and IV) to investigate the addition-elimination reaction process. Paths I and III are the additions of only one •OH radical at C atoms in the imidazole ring followed by the release of nitro and methyl radicals, while paths II and IV are the additions of two •OH radicals at different positions in the ring, and their elimination products are nitric acid and methanol, respectively. The first route, path I, adding •OH to the ring followed by the elimination of CH3, has a barrier of 36.7 kcal/mol, as seen in Fig. 10, and the energy of the final products (B+CH3) is 1.7 kcal/mol lower than that of initial reagents (MNZ+•OH). It is worth noting that, from A to B, the energy is rising, which means that it needs to 18


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absorb energy to reach the relatively stable state (B+CH3). The second route (Path II) has a different result, that is, although it has a 54.8 kcal/mol energy barrier, it generates more stable products (B+CH3OH: -82.7 kcal/mol below the initial state). Besides, the gap between the transition state energies of these two paths and that of their reagents are 12.5 kcal/mol for the former and 17.7 kcal/mol for the latter. Fig. 9 Fig. 10

Nitro elimination reaction. Similarly, two routes for nitro elimination reactions (Path III and Path IV) are studied in the following part. Unlike methyl elimination, this type of reaction appears to occur more easily through a single •OH addition reaction. As shown in Fig. 11, the addition and elimination reaction with a single •OH requires almost no barrier energy (0.12 kcal/mol), while that with double •OH radicals has an energy cost of 63.6 kcal/mol. The process from E to F is exothermic (-7.1 kcal/mol), whereas that from E’ to F is endothermic (29.7 kcal/mol). Compared with the initial states (MNZ plus one or two •OH), both complete reaction processes are exothermic. Even at the highest points (TS), the energies are much lower than that of the methyl elimination reactions. Evidently, compared with methyl, -NO2 is much easier to be replaced by •OH. The results are consistent both with that obtained by the SMF fragmentation model, in a purely statistical physics frame, and with the product identified in 19



the experiments18, that is 3-(2-hydroxy-ethyl)-2-methyl-3H-imidazol-4-ol (the molecule F in Fig. 11) produced by the replacement of –NO2 by •OH rather than 1-(2-hydroxyethyl)-5-nitro-1H-imidazol-2-ol (the molecule B in Fig. 10) produced by the replacement of –CH3 by •OH. Fig. 11

Dissociation of –CH2CH2OH. In view of the possibility of –CH2CH2OH released from MNZ obtained by the SMF model, a scanning task was executed to simulate the breaking process of –CH2CH2OH. The reaction was simplified as a bond-breaking reaction with the dissociation of –CH2CH2OH group. The results are showed in Fig. 12. The upper limit value of the activation energy could be used as an energy barrier, although it is not very accurate. From Fig. 12, we can see that the dissociation of –CH2CH2OH has a barrier energy of about 51 kcal/mol, where the length of atom N and C is 2.07 Å. After the dissociation of –CH2CH2OH, hydroxyl radical would append to the remaining molecule. Compared with the alcohol group oxidation and nitro elimination reaction, the energy barrier of the dissociation of –CH2CH2OH is higher, indicating that it is more difficult for hydroxyl radical to substitute –CH2CH2OH on MNZ. Fig. 12

In this section, we have analyzed in detail the possible degradation pathways 20


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of MNZ, which include the oxidation of the –CH2OH group, addition-elimination reactions and the dissociation of –CH2CH2OH. To sum up, the oxidation of the –CH2OH group mainly includes the mechanism of hydrogen-abstraction through two routes: one is the H-abstraction from the O atom and the other is the H-abstraction from the C atom, in the first step. The highest activation barriers in both paths are 59.6 kcal/mol and 39.1 kcal/mol, respectively, suggesting that the second route is more likely to happen. Four routes of addition-elimination mechanisms for the degradation of MNZ by •OH were calculated. During the methyl elimination reactions, the energy barriers are 36.7 and 54.8 kcal/mol for the addition of a single •OH radical and double •OH radicals, respectively. There is almost no obstacle to the replacement of -NO2 by •OH, implying that this step happens easily. The addition-elimination reaction of double •OH radicals for the replacement of -NO2 requires a barrier energy of 63.6 kcal/mol. However, the former exothermic reactions release enough heat to make the reaction overcome the obstacle. Accordingly, the primary degradation step of MNZ is easy to occur, and the addition of •OH with the elimination of -NO2 should be a main reaction channel.

CONCLUSIONS In summary, the primary elimination process of metronidazole has been studied within the statistical physics schemes and with a transition state analysis, both using the M06-2X/6-311+G(d,p) level. The results calculated by 21



the SMF model show that the minimum dissociation energy of MNZ is 82.7 kcal/mol, which corresponds to the fragmentation of NO2 (release of NO2 and, on a narrow range, of O), representing the main fragmentation process below the three-fragment threshold (115 kcal/mol). Over 100 kcal/mol, CH2OH radicals and then CH2CH2OH radicals are released. The SMF model also predicts that below 115 kcal/mol, neither hydrogen atoms nor CH3 molecules are generated in the fragmentation of MNZ. The DFT transition state study leads to the proposed reaction pathways that are multistep exothermic processes, and neither of these routes (addition-elimination reaction in N3 and hydrogen-abstraction reaction in C17) requires high energy barriers, thus they occur spontaneously. TS analysis leads to the same conclusion as SMF about the prevalence of the NO2 release channel. On the other hand, the d18+H and d21+H hydrogen-abstraction channels are predicted to be negligible in gas phase by the SMF model, which shows that they happen only thanks to the lowering of the barriers due to •OH radicals in the aqueous phase. The results are in good agreement with the experiments, that is, during the degradation process, the nitro elimination reaction and the oxidation of the hydroxyl group to the carboxylic acid are more likely to occur than other radical group eliminations. The details of structural information can help us understand the degradation mechanisms of MNZ. The information about the reaction mechanisms obtained by these theoretical calculations is in turn essential for improving the reduction efficiency of MNZ by AOPs in actual treatment 22


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processes.

ACKNOWLEDGEMENTS The authors wish to thank Dr. Dominik Domin for fruitful discussions and careful reading of the manuscript. This work was supported by the National Natural Science Foundation of China (Grant No. 51708238) and the National Natural Science Foundation special fund for Thousands Plan Youth Talent (No. 0222120003; 0214120048).

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31



Figure captions Fig. 1. The structure and atom labels of MNZ with bond lengths, bond dissociation energies (BDE) and Mulliken charges (labeled in green).

Fig. 2. Statistical weights, as a function of excitation energy, for all metronidazole fragmentation channels with one or two fragments (d3+NO2 signifies the cleavage of C3−N5 bond on the chain of C3 atom as seen in Fig. 1, releasing NO2; other naming methods are similar).

Fig. 3. Probabilities, as a function of excitation energy, for metronidazole fragmentation channels with one or two fragments.

Fig. 4. The possible degradation pathways for MNZ reacting with •OH based on the results calculated by the SMF model as well as the intermediates detected by experiments: (a) alcohol group oxidation, (b) addition-elimination reaction.

Fig. 5. Two pathways for the oxidation of the alcohol group on MNZ by •OH.

Fig. 6. Optimized geometries of TS0, TS0’, TS1, TS1’ and TS2 for the oxidation of the alcohol group on MNZ by •OH with select distance values (li, i = 1, 2, 3) given in Å. 32


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Fig. 7. Free energy profiles for the oxidation of the alcohol group on MNZ by •OH, and two pathways marked in black and in red from 0 to 2. The relative free energies are calculated, considering the reaction balance equations.

Fig. 8. The free energies (∆G) and geometries of four isomeric intermediates generated by the addition of a •OH radical. Reference energy (0 kcal/mol) is the sum of Gibbs free energies of the MNZ and of the •OH radical.

Fig. 9. Addition-elimination mechanisms for the degradation of MNZ by •OH.

Fig. 10. Calculated energy profiles for the methyl-elimination reactions.

Fig. 11. Calculated energy profiles for the nitro-elimination reactions.

Fig. 12. A potential energy surface for the dissociation of –CH2CH2OH group from MNZ. The variation of total energy (kcal/mol) is given to crudely estimate the free-energy barrier.

33



Page 34 of 49

Figure 1

N2

N3 N8

34


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Figure 2

35



Figure 3

36


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Figure 4

37



Figure 5

38


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Figure 6

39



Figure 7

40


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Figure 8

41



Figure 9

42


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Figure 10

43



Figure 11

44


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Figure 12

45



Page 46 of 49

Table 1. Heterocyclic intermediates and hydroxylated derivatives identified and deduced by LC/MS and GC/MS.10, 12, 18, 19 Number

Name

Structure

1

3-(2-Hydroxy-ethyl)-2-methyl-3H-imidazol-4-ol

2

(2-Methyl-5-nitroimidazol-1-yl) acetic acid

3

(5-Hydroxy-2-methyl-imidazol-1-yl) acetic acid

4

2-Methyl-5-nitro-1H-imidazole

5

2-Methyl-3H-imidazol-4-ol

6

1-(2-Hydroxyethyl)-2-methyl-5-aminoimidazole

7

1-(2-Hydroxyethyl)-2-methyl-5-imidazole

8

1H-imidazole

9

(5-Hydroxy-1H-imidazol-1-yl) acetic acid

10

1H-imidazol-5-ol 46


Page 47 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46


Table 2. The input table for the SMF model (DFT at the M06-2X/6-311+G(d,p) level). molecule

e- spin m.

charge

2Le+1

Symmetry fac.

Hth (Ha)

𝝎 (Ha)

fr

fv

Ix (a.u.)

Iy (a.u.)

metronidazole

s

0

1

1

-623.630

3.86 m

3

57

5.58 M

3.76 M

d3

d

0

1

1

-418.461

4.18 m

3

48

3.80 M

d4

s

0

1

1

-548.438

3.95 m

3

54

d5

s

0

1

1

-548.440

3.99 m

3

d7

d

0

1

1

-622.949

3.74 m

d10

d

0

1

1

-583.663

d11

d

0

1

1

d14

d

0

1

d15

d

0

d17

d

d18

m (me-)

Ed min (Ha)

2.52 M

312 k

132 m

3.08 M

1.01 M

228 k

114 m

4.82 M

3.23 M

2.21 M

282 k

103 m

54

4.49 M

2.68 M

2.47 M

282 k

105 m

3

54

5.51 M

3.75 M

2.46 M

310 k

131 m

3.68 m

3

45

5.27 M

3.84 M

1.66 M

284 k

124 m

-622.990

3.74 m

3

54

5.70 M

3.72 M

2.47 M

310 k

127 m

1

-469.221

3.54 m

3

33

3.59 M

2.87 M

7.37 M

230 k

106 m

1

1

-622.974

3.67 m

3

54

5.94 M

4.26 M

2.23 M

310 k

124 m

0

1

1

-508.495

3.80 m

3

42

4.13 M

3.02 M

1.13 M

255 k

126 m

d

0

1

1

-622.984

3.67 m

3

54

5.56 M

3.69 M

2.56 M

310 k

115 m

d20

d

0

1

1

-547.761

3.74 m

3

51

4.79 M

3.15 M

1.89 M

281 k

127 m

d21

d

0

1

1

-622.969

3.77 m

3

54

5.52 M

3.66 M

2.52 M

310 k

18.4 m

H

d

0

1

0

-0.496

0

0

0

0

0

0

1.84 k

0

O

s

0

1

0

-74.963

0

0

0

0

0

0

29.1 k

0

O

t

0

1

0

-75.059

0

0

0

0

0

0

29.1 k

0

OH

d

0

1

1

-75.715

16.6 m

2

1

5.83 k

5.83 k

0

31.0 k

160 m

CH3

d

0

1

3

-39.787

7.77 m

3

6

22.9 k

11.4 k

11.4 k

27.4 k

171 m

CH2OH

d

0

1

1

-115.001

6.34 m

3

9

125 k

109 k

17.0 k

56.5 k

49.0 m

CH2CH2OH

d

0

1

1

-154.269

5.26 m

3

18

384 k

326 k

81.8 k

82.1 k

46.5 m

NO2

d

0

1

2

-205.038

5.62 m

3

3

261 k

248 k

13.0 k

83.8 k

107 m

47


Iz (a.u.)


Page 48 of 49

Table 3. The calculated Gibbs free energies of reaction (∆GR) and activation energies (∆G) at 298.15 K for all reactions in Fig. 5 (kcal/mol). Reaction step

∆GR

∆G

Reaction step

∆GR

∆G

0+•OH→IN1+H2O

-11.9

59.6

1+•OH→2+H2O

-67.2

57.2

0+•OH→IN1’+H2O

-22.6

5.3

1’+•OH→2+H2O

2.1

39.1

IN1+•OH→1

-26.7

−

2+•OH→IN2+H2O

-25.6

3.2

IN1’+•OH→1’

-85.3

−

IN2+•OH→3

-94.4

−

48


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TOC Graphic:

49


A Statistical Model and DFT Study of the Fragmentation Mechanisms

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